Details

Time bar (total: 3.7s)

analyze4.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%0%100%0
0%0%100%1
Compiler

Compiled 30 to 17 computations (43.3% saved)

sample44.0ms (1.2%)

Algorithm
1×intervals
Results
27.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 51 to 29 computations (43.1% saved)

simplify187.0ms (5.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0121736
1121736

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.7b

Counts
2 → 1
Compiler

Compiled 42 to 20 computations (52.4% saved)

localize29.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 x PI.f32)
0.4b
(/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 (*.f32 x PI.f32) tau))
0.4b
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))

rewrite29.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
22×add-cbrt-cube_binary32_447 add-exp-log_binary32_449
16×add-sqr-sqrt_binary32_435
12×add-cube-cbrt_binary32_446 *-un-lft-identity_binary32_414
8×pow1_binary32_472
6×cbrt-unprod_binary32_444 associate-*l*_binary32_357 associate-/l*_binary32_361 associate-*r*_binary32_356 times-frac_binary32_420 prod-exp_binary32_460
5×div-exp_binary32_462 cbrt-undiv_binary32_445
4×add-log-exp_binary32_450
2×div-inv_binary32_411 pow-prod-down_binary32_482 clear-num_binary32_413 unswap-sqr_binary32_382 associate-/r*_binary32_360 frac-2neg_binary32_425 *-commutative_binary32_347
Counts
4 → 80
Calls

4 calls:

8.0ms
(/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 (*.f32 x PI.f32) tau))
6.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
4.0ms
(*.f32 x PI.f32)
4.0ms
(*.f32 x PI.f32)

series203.0ms (5.6%)

Counts
4 → 12
Calls

4 calls:

79.0ms
(/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 (*.f32 x PI.f32) tau))
72.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
27.0ms
(*.f32 x PI.f32)
24.0ms
(*.f32 x PI.f32)

simplify76.0ms (2.1%)

Algorithm
1×egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049771324
149771324

prune111.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New801292
Fresh000
Picked101
Done000
Total811293

Merged error: 0.2b

Counts
93 → 12
Compiler

Compiled 2657 to 462 computations (82.6% saved)

localize37.0ms (1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 x PI.f32)
0.4b
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
0.5b
(*.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (/.f32 1 (*.f32 (*.f32 x PI.f32) tau)))

rewrite36.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
45×add-exp-log_binary32_449
27×add-cbrt-cube_binary32_447
22×prod-exp_binary32_460
19×add-sqr-sqrt_binary32_435
13×add-cube-cbrt_binary32_446 associate-*r*_binary32_356 *-un-lft-identity_binary32_414
10×cbrt-unprod_binary32_444 pow1_binary32_472
9×associate-*l*_binary32_357
8×div-exp_binary32_462
6×times-frac_binary32_420
5×cbrt-undiv_binary32_445
4×add-log-exp_binary32_450
3×1-exp_binary32_455 pow-prod-down_binary32_482 unswap-sqr_binary32_382 rec-exp_binary32_461 associate-/l*_binary32_361 *-commutative_binary32_347
2×div-inv_binary32_411
1×un-div-inv_binary32_412 clear-num_binary32_413 associate-*r/_binary32_358 associate-/r*_binary32_360 frac-2neg_binary32_425
Counts
4 → 93
Calls

4 calls:

13.0ms
(*.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (/.f32 1 (*.f32 (*.f32 x PI.f32) tau)))
5.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
4.0ms
(*.f32 x PI.f32)
4.0ms
(*.f32 x PI.f32)

series196.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

80.0ms
(*.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (/.f32 1 (*.f32 (*.f32 x PI.f32) tau)))
69.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
24.0ms
(*.f32 x PI.f32)
23.0ms
(*.f32 x PI.f32)

simplify68.0ms (1.9%)

Algorithm
1×egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050101558

prune104.0ms (2.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1032105
Fresh01111
Picked101
Done000
Total10413117

Merged error: 0.2b

Counts
117 → 13
Compiler

Compiled 3154 to 740 computations (76.5% saved)

localize36.0ms (1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 x PI.f32)
0.4b
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))

rewrite24.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
18×add-sqr-sqrt_binary32_435
15×add-cbrt-cube_binary32_447 add-exp-log_binary32_449
12×add-cube-cbrt_binary32_446 *-un-lft-identity_binary32_414
10×pow1_binary32_472
9×associate-*l*_binary32_357 associate-*r*_binary32_356
4×add-log-exp_binary32_450 cbrt-unprod_binary32_444 prod-exp_binary32_460
3×pow-prod-down_binary32_482 unswap-sqr_binary32_382 associate-/l*_binary32_361 times-frac_binary32_420 *-commutative_binary32_347
2×div-exp_binary32_462 cbrt-undiv_binary32_445
1×div-inv_binary32_411 clear-num_binary32_413 associate-/r*_binary32_360 frac-2neg_binary32_425
Counts
4 → 75
Calls

4 calls:

6.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
4.0ms
(*.f32 x PI.f32)
4.0ms
(*.f32 x PI.f32)
4.0ms
(*.f32 x PI.f32)

series132.0ms (3.6%)

Counts
4 → 12
Calls

4 calls:

61.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
25.0ms
(*.f32 x PI.f32)
23.0ms
(*.f32 x PI.f32)
22.0ms
(*.f32 x PI.f32)

simplify72.0ms (2%)

Algorithm
1×egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
05502878

prune85.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New85287
Fresh11112
Picked101
Done000
Total8713100

Merged error: 0.2b

Counts
100 → 13
Compiler

Compiled 2505 to 463 computations (81.5% saved)

localize38.0ms (1%)

Local error

Found 4 expressions with local error:

0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 x PI.f32)
0.4b
(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 x PI.f32)) (/.f32 1 tau))
0.4b
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))

rewrite41.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
52×add-exp-log_binary32_449
34×add-cbrt-cube_binary32_447
30×add-sqr-sqrt_binary32_435
20×*-un-lft-identity_binary32_414
19×add-cube-cbrt_binary32_446 associate-*r*_binary32_356 prod-exp_binary32_460
17×times-frac_binary32_420
16×div-exp_binary32_462
13×associate-*l*_binary32_357
11×cbrt-unprod_binary32_444
10×pow1_binary32_472
9×cbrt-undiv_binary32_445
5×unswap-sqr_binary32_382
4×add-log-exp_binary32_450
3×div-inv_binary32_411 1-exp_binary32_455 pow-prod-down_binary32_482 rec-exp_binary32_461 associate-/l*_binary32_361 *-commutative_binary32_347
1×un-div-inv_binary32_412 frac-times_binary32_424 clear-num_binary32_413 associate-*r/_binary32_358 associate-/r*_binary32_360 frac-2neg_binary32_425 associate-*l/_binary32_359
Counts
4 → 111
Calls

4 calls:

16.0ms
(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 x PI.f32)) (/.f32 1 tau))
6.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
4.0ms
(*.f32 x PI.f32)
4.0ms
(*.f32 x PI.f32)

series188.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

76.0ms
(*.f32 (/.f32 (sin.f32 (*.f32 (*.f32 x PI.f32) tau)) (*.f32 x PI.f32)) (/.f32 1 tau))
62.0ms
(/.f32 (sin.f32 (*.f32 x PI.f32)) (*.f32 x PI.f32))
26.0ms
(*.f32 x PI.f32)
24.0ms
(*.f32 x PI.f32)

simplify98.0ms (2.7%)

Algorithm
1×egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049592022
149592022

prune104.0ms (2.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1221123
Fresh01212
Picked011
Done000
Total12214136

Merged error: 0.2b

Counts
136 → 14
Compiler

Compiled 3284 to 656 computations (80% saved)

regimes95.0ms (2.6%)

Compiler

Compiled 1195 to 583 computations (51.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01939
11939

end0.0ms (0%)

sample1.6s (44.1%)

Algorithm
1×intervals
Results
884.0ms8000×body128valid
190.0ms8000×pre128true
Compiler

Compiled 448 to 221 computations (50.7% saved)

Profiling

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